It was one of the most gruesome killings in Greater Boston in many years: three young men found with their throats slit inside a Waltham apartment on a quiet residential street, their bodies sprinkled with marijuana.

Now, police and prosecutors are stepping up their investigation into the unsolved 2011 triple homicide at the request of victims’ relatives who believe that suspected Marathon bomber Tamerlan Tsarnaev may have played a role, noting that Tsarnaev had been close friends with one of the dead men.

What is more, the grieving relatives say the killings took place on a highly symbolic date for Islamic extremists: the 10th anniversary of the 9/11 attacks on the World Trade Center and the Pentagon.

“We’re eager to pursue any new leads or information,” said Stephanie Guyotte, spokeswoman for the Middlesex district attorney’s office. “It has been reported that [Tamerlan Tsarnaev] knew one of the deceased victims. It remains an open investigation.”

Get Fast Forward in your inbox:

Forget yesterday's news. Get what you need today in this early-morning email.

The death certificates of two of the victims — Brendan H. Mess, 25, and Rafael M. Teken, 37 — say they were killed on Sept. 12, the day that Mess’s girlfriend reportedly discovered the bodies of the three victims and ran screaming from the two-family house where they had gathered.

But a relative of one of the victims told the Globe he is certain they were killed on the evening of Sept. 11, because he was texting one of them about a Sunday night football game between the New York Jets and Dallas Cowboys when communication suddenly stopped, at about 8:15 that evening.

He also said that, after speaking with relatives and friends of the other two victims, he concluded that communication with all of the victims was shut down at about the same time.

“The three of them were definitely killed on Sept. 11,” the relative said. “They all stopped using their cellphones at about eight o’clock that night.”

The relative asked for anonymity because other family members agreed they would not speak to the news media, pending the outcome of their recent communication with authorities.

The Globe reported Saturday that Tamerlan Tsarnaev knew Mess well, once introducing him to the owner of the gym where they both worked out as his “best friend.” But another friend of Mess said Tsarnaev did not attend Mess’s funeral.

“If they were best friends, you would think [Tamerlan] would have been absolutely devastated and would have reached out to someone,” said the friend of Mess, who asked not to be identified for fear of retaliation. “That confirms my suspicions that something was up.’’

Records reviewed by the Globe show that at least one member of the Mess family lived in the same Cambridge neighborhood as the Tsarnaevs.

People who knew Tamerlan Tsarnaev, who died at 26 years of age in a firefight with police last week, say that he turned to radical Islam a year or two before the Waltham slayings, growing a long beard, adopting Islamic dress, and apparently posting extremist videos on YouTube.

In 2011, FBI agents questioned Tsarnaev after his native Russia raised concerns about his possible extremism.

In addition, within months of the triple homicide, in early 2012, In 2011, FBI agents questioned Tsarnaev went to Russia for six months, visiting family members in Dagestan, which borders the Tsarnaevs’ ancestral homeland of Chechnya, a region with a history of violent Islamic rebellion.

In light of the bombings on Marathon Monday, the Waltham homicide victim’s relative said, he and other victims’ relatives believe that Tsarnaev’s younger brother, Dzhokhar, the second suspected Marathon bomber, might also have played a role in the homicides because of the difficulty that one killer would face subduing the three victims, at least two of whom were in good physical condition.

Police never identified any suspects in the case, but the person or persons who committed the slayings had to be strong and highly skilled.

On the death certificates, Mess is listed as a martial arts instructor and is known to have trained at the same gym as Tsarnaev, Wai Kru Mixed Martial Arts, in Allston. Teken is listed as a personal trainer. The Globe was unable to obtain the death certificate for the third victim, 31-year-old Erik Weissman.

In addition to the marijuana and $5,000 found at the crime scene, Weissman’s past may have pointed investigators to drugs as a motive. In 2008, Weissman was charged with possession of marijuana with intent to distribute, according to a police report.

Whatever the reason for the killings, Tamerlan Tsarnaev, an accomplished amateur heavy-weight boxer, certainly had the physical strength to carry out a brutal attack. “He was the best boxer in Boston,” said John Allan, the owner of Wai Kru Mixed Martial Arts. “He smoked all the professionals.”

And Tsarnaev had already demonstrated a violent streak outside of the ring: In 2009, he was charged with domestic violence after admitting to police that he had slapped a former girlfriend, who then called police in hysterics. The charge was later dismissed after a jury trial.

Younger brother Dzhokhar, meanwhile, had been captain of the Cambridge Rindge and Latin wrestling team and was also known as an adept boxer, according to Zolan V. Kanno-Youngs, a neighbor, friend, and former classmate.

And during the months before the killings, it is clear that Tsarnaev had become increasingly radicalized in his religious and political beliefs.

Maret Tsarnaeva, Tsarnaev’s aunt, told reporters at a news conference that her nephew went from praying no more than once a day to praying five times a day. And a neighbor and family friend in Cambridge said Tsarnaev had become a devout Muslim within the past few years.

“He started talking about religion,” said the family friend, who asked not to be identified. “He grew a long beard.”

When the friend joked about the beard, he said, Tamerlan became upset, asking, “Why are you making fun of my religion?”

It appears that Tsarnaev also toyed with extremism online. A YouTube account created in Tamerlan Tsarnaev’s name in August 2012 includes a video dedicated to the prophecy of the Black Banners of Khurasan, which is apparently embraced by Islamic extremists.

In another video, featured on a play list titled “terrorists,” a speaker holds an assault rifle and wears camouflage fatigues while flanked by armed men wearing masks.

The relative of the Waltham homicide victim interviewed by the Globe said he and others hope their recent appeal to police about Tamerlan Tsarnaev’s possible role in the killings will lead to a conclusion of the case.

BostonGlobe.com complimentary digital access has been provided to you, without a subscription, for free starting today and ending in 14 days. After the free trial period, your free BostonGlobe.com digital access will stop immediately unless you sign up for BostonGlobe.com digital subscription. Current print and digital subscribers are not eligible for the free trial.

Thanks & Welcome to Globe.com

You now have unlimited access for the next two weeks.

BostonGlobe.com complimentary digital access has been provided to you, without a subscription, for free starting today and ending in 14 days. After the free trial period, your free BostonGlobe.com digital access will stop immediately unless you sign up for BostonGlobe.com digital subscription. Current print and digital subscribers are not eligible for the free trial.